Crooked Timber

I spent some time in the departure lounge of Calgary airport on Friday, with Agustin “the Mexican Multiplier” Rayo and JC Beall, and JC mentioned how annoying he found it that some philosophers used the expressions “philosophical logic” and “philosophy of logic” interchangably. In fact, he thought he might write something up about it and try to get people to take notice. Not being one to stomp on a worthy cause, I asked him whether he’d let me post such a thing to a blog. He agreed, and so I give you JC’s Column (an occasional series?) Reform or perish…

There’s reason to think that confusion exists over the terminology of “philosophical logic” and “philosophy of logic”. It would do the profession — and, perhaps, aspiring graduate students — well to have uniform terminology. While terminological differences certainly exist across the English-speaking countries (e.g., in parts of the UK, “philosophical logic” is often synonymous with “philosophy of logic”, though not so in Oz), here is a fairly standard — though admittedly (perhaps perforce) vague — classification, one that, if broadly adopted, would at least diminish some of the confusion.

A. Formal Philosophy: formal (mathematical) methods used in the service of philosophy.

(This comprises a lot, including philosophical logic, some areas of mathematical logic, decision theory, what Branden calls “formal epistemology”, some areas of foundations of mathematics, some incarnations of philosophy of logic, some incarnations of philosophy of language, and much more. Similarly, some work in metaphysics — particularly, formal ontology, formal mereology, etc. — would certainly fall under this banner. So, this category is perhaps the broadest category, but it’s worth including here. What is crucial is that formal, mathematical methods — as opposed to just using symbols as abbreviations, etc. (!) — is essential.)

B. Philosophical Logic: formal logic (usually, applied maths) in the service of philosophy; in particular, a formal account of consequence for some philosophically interesting fragment of discourse.

[If we take Logic to be concerned with consequence, then philosophical logic aims to specify — in a formal, precise way — the consequence relation over some philosophically significant fragment of our language. (Usually, this is done by constructing a formal “model language”, and proposing that the logic of the target “real language” is relevantly like that.) Usually, philosophical logic overlaps a lot with formal semantics, but may often be motivated more by philosophical concerns than by linguistic data. Work on formal truth theories — i.e., specifying the logic of truth — is a familiar example of work in philosophical logic, as are the familiar modal and many-valued accounts of various expressions, and similarly concerns about ‘absolute generality’ and the consequence relation governing such quantification, and much, much else. What is essential, as above, is a specification of a given consequence relation for the target, philosophically interesting phenomenon. Whether the consequence relation is specified “semantically”, via models, or proof-theoretically is not critical — although the former might often prove to be heuristically better in philosophy.]

C. Philosophy of Logic: philosophy motivated by Logic; philosophical issues arising out of a given, specified logic (or family of logics).

[While competence in (formal) logic is often a prerequisite of good philosophy of logic, no formal logic or, for that matter, formal methods need be involved in doing philosophy of logic. Of course, philosophy of logic often overlaps with philosophy of language — as with many areas of philosophy. The point is that philosophy of logic, while its target may be mathematical or formal, needn’t be an instance of either philosophical logic — which essentially involves formal methods — or, more broadly, formal methods. A lot of work on “nature of truth” might be classified as philosophy of logic (though much of it probably isn’t motivated by logic, and so shouldn’t be so classified), and similarly for “nature of worlds” etc. Whether the classification is appropriate depends, in part, on the given project — e.g., whether, as with Quine and Lewis, one is directly examining the commitments of a particular logical theory, as opposed to merely reflecting on “intuitions” concerning notions that are often thought to be logically significant. The point, again, is just that philosophy of logic is a distinct enterprise from philosophical logic, each requiring very different areas of competence, and each targeted at different aims.]

It would be useful if the profession, in general, but especially practitioners adopted terminology along the above lines. Of course, there’s still room for confusion, and the foregoing hardly cuts precise joints. It might be useful to discuss refinements to the above terminological constraints.

One more — just for those who might be wondering:

D. Mathematical Logic: formal logic in the service of (usually classical!) mathematics, as well various subfields of mathematics. (E.g., standard limitative theorems and classical metatheory is mathematical logic, as is reverse mathematics, many aspects of category theory, many aspects of set theory, areas of abstract algebra, areas of recursion theory, and so on. Mathematicians need have no interest in philosophy to engage in such areas, in contrast with the philosophical logician who is driven to use “mathematical methods” in an effort to clarify the consequence relation of some philosophically interesting “discourse”. There’s more to be said here, but this is chiefly a post about A, B, and C.)

One note: it may well be that anyone talented in B is interested in C, but it hardly follows that one who is talented in B is talented in C. Similarly, one who is talented in C may well have little talent or interest in B. My hunch is that, on the whole, those who do B (or do it well) are usually talented in C. It’s unclear whether those with a talent in D are naturals for B or C — or A, for that matter — but one can think of excellent philosophers who also engaged directly in D. (The obvious such folks were also good at A, B, and C, as well as D. Russell comes to mind, as does Kripke, but there are others.)

First a bleg. Those of you who read over there may have noticed that I haven’t posted at my other blog in a few weeks. At first it was just the usual not having the right combination of time and ideas, but recently the software has given me trouble again, and now doesn’t believe that there’s a blog there for me to edit. (Fortunately it’s still displaying all the old posts.) So I’m planning on moving away from MovableType. But since I can’t log in to export the old posts, I was wondering if anyone knows of a way to extract them efficiently so I can host them on different software, possibly on a different site. (I lost control of antimeta.org about a year ago when I switched hosting companies, and they seem to have accidentally renewed the registration, so I may have to change domain names again.)
Anyway, I was just in Banff for probably the most blogged-about conference I’ve ever been to. I count nine posts between , Gillian, and Richard, as well as twomentions on Certain Doubts. Also, I believe Aldo Antonelli got a lot of good pictures, including one of Gillian and me that should appear in the upper-left corner here at some point after I get a copy from either him or Richard Zach.
I found it to be a great workshop, and I’m very glad that Richard invited me! Despite the very broad “focus” on mathematical methods in any area of philosophy, there were some very interesting series of talks that gave some coherent threads. For instance, theories of truth were the focus of the survey by JC Beall and Michael Glanzberg, as well as more specific talks by Volker Halbach, Jeff Ketland, Sol Feferman, and Greg Restall. And a variety of different semantics for modal logics (especially quantified and non-classical) were discussed by Marcus Kracht, Steve Awodey, Eric Pacuit, Greg Restall, and Graham Priest. There were also two interesting proposals, by Delia Graff Fara and Kai Wehmeier, suggesting that identity as a relation doesn’t play quite the role we think it does, the former pointing out that for a lot of purposes (especially modal and temporal ones) we can’t use strict identity, but rather some “same F as” relation; the latter arguing that identity shouldn’t even be treated as a relation in logic at all!

Given my experiences at FEW (abstract deadline today if you want to submit!) I was surprised by a relative lack of talks on probability (basically only Branden Fitelson and Tim Williamson, and one fourth of Hannes Leitgeb’s virtuoso four talks in one hour performance). But there’s always got to be some trade-off. Anyway, I had lots of productive conversations (some while cross-country skiing) that will shape my dissertation, some papers I’ve been working on, and almost certainly some future blogposts either here or wherever I get my other blog working once I can transfer the old posts.

Ned Hall has a paper in a recent Philosophical Studies where he defends a new account of causation. The crucial idea is that we have to distinguish between default and deviant states for certain events/objects. Applied to simple cases like neuron diagrams, the default state of a neuron is to not fire. The theory gets a few complicated cases right, but it seems to not get some even more complicated right. I’ll state (hopefully not too badly) the theory, then offer a counterexample to it. There’s a little bit of interpretation here, because Hall never quite states the theory like this, so I might be horribly misinterpreting something.

C is a cause of E iff there are some events K such that

each event in K consists of some entity being in a deviant, rather than a default, state

had every event in K not happened, E would still have happened

had every event in K not happened, every event in the causal network of which C and E are parts either would have happened in the same way, or would have reverted to its default state

had every event in K not happened, E would have been counterfactually dependent on C

Here is a kind of counterexample to it. First the diagram, then the description.

A sets off a chain of events that, if unchecked, will result in E.

B initiates a threat to E.

C causes the threat to be cancelled early.

C also initiates a chain that, if left unchecked, will cancel the threat late.

D pre-empts this second chain, and will cancel the threat late if it is still present.

C causes E by defusing a threat to it, but it fails Hall’s test. E isn’t counterfactually dependent on C. If D hadn’t happened, E would have been counterfactually dependent on C. But if D hadn’t happened, an event that is actually at default, the one labelled G on the diagram, would have been in a deviant state. So there is no set K as required above, and C is not a cause of E. But this is wrong, since C is what defuses the threat to E.

I think there are also cases where Hall’s theory mistakenly classifies a non-cause as a cause, but those cases are more contentious and I’ll leave them for another post.

We have some excellent news to report here at Cornell. Karen Bennett, currently at Princeton, has agreed to join the Sage School starting in Fall semester this year. Karen has produced some impressive works in philosophy of mind and in metaphysics. See, for example, her papers on actualism and the exclusion problem. So we’re very excited that she agreed to move to Cornell.

Cornell is starting to specialise in hiring people at or around tenure time. In recent years it’s hired Delia Graff Fara, Tamar Gendler, me, Matti Eklund, Michelle Kosch and now Karen Bennett. That’s a pretty good list I’d say, even if the first two people on it have since been lured away. There has been a lot of discussion around the places about the excellent people Cornell has recently lost, but those we’ve hired are pretty talented too. Of course as well as the people listed here we’ve hired Nico Silins and Derk Pereboom just recently, and Andrew Chignell not long ago, so it’s not just at the tenure stage that we’re hiring well.

I should note that this news is a little old by blog standards, since Karen agreed to join the department last week. But this happened while I was away – while I was stuck on the clogged Pennsylvania highways the day after the big snowstorm – so I’ve only just had the chance to announce it now.

Do not be deceived, Establishment pigs (this means you too, Establishment dogs). The subservience of past generations of logicians does not mean that we shall bear forever our treatment as animals (you barnyard fowl). We are human beings (you swine). You are living in a day when logicians will not any longer endure your taunts, your slurs, your insults (you filthy vermin). In the name of A. N. Whitehead and B. Russell we gather; in the spirit of R. Carnap and A. Tarski, we march; by the word of W. V. O. Quine, we shall prevail. Beware you snakes of the Philosophical Power Structure, which you have created and which you maintain to put down the logician; you have caged the eagle of reason, the dove of wisdom, and the lark of a definite, precisely formulated formal system, with exact formation rules, a recursive set of axioms, and clear and cogent rules of inference, and you have made them your pigeons. Oh, you filterable viruses, we will shake you off and fly once more.

(I’ve just realised – in searching for the text – that Greg Restall is blogging about the conference too. I guess reporting on this one is kind of overdetermined – look out for further posts from Richard Zach too. Greg has his laptop in the sessions, so that might be the place to go for the most up-to-the-minute reporting! I’m pretty amazed that Google had him linked already though – those little Googlebots must be much faster than they used to be.)

Branden also announced that the Stanford Encyclopedia of Philosophy is widening its “Inductive Logic and Decision Theory” area to “Formal Epistemology”, with Branden Fitelson and Al Hajek joining Briain Skryms and Jim Joyce as editors.

And finally, he also said that Studia Logica is changing its broadening its scope to include “Formal Philosophy”, and there are several new editors with special issues coming up, including:

Leitgeb: Psychologism in Philosophy

Douven and Horsten: Applied Logic in Philosophy of Science

Behounek and Keefe: Vagueness

Fitelson: Formal Epistemology

According to Branden, the scope of “Formal Epistemology” is everything in formal philosophy that isn’t metaphysics. Except that it also includes the foundations of probability. That doesn’t leave a lot out, so if you have a good formal paper and you were wondering whether it would fit…it probably does.

OK, I’m off to walk through snowy pines before coming back to hot chocolate and JC Beall and Michael Glanzberg talking about paradoxes. (Did I mention that the programme is amazing?) Wish you were here…

So I’ve been spending time that I should be spending writing about disagreements about taste, fragmented belief, perception, and funny kinds of context dependence, thinking instead about a lyric from a Black Eyed Peas song (“Latin Girls”) that I was listening to while surfing the web writing about all of the very important topics that I ought to be writing about. Anyway, here’s the lyric:

“Girl, you know I know you know what I mean.”

And I started wondering (as one does):

(a) What’s the difference between the overall communicative effects of asserting,

(i) You know what I mean
and
(ii) You know I know you know what I mean

(b) Whatever the differences are, can you get an adding-to-common-knowledge view of assertion to predict them?

I started thinking about this after Aidan Lyon‘s excellent talk on the curve-fitting problem here at the ANU yesterday.

Graham Priest in his 1976 article Gruesome Simplicity (this link is to JSTOR) discusses curve-fitting as a way of making inductive inferences. When we plot observed values of two related quantities x and y on a graph, we have several options for which curve to draw between them. The simplicity of the curve has to be traded off against fit with the existing data points, and it is a taxing problem to say how best this should be done. Yet we often do think we can choose an appropriate curve, and use it to make predictions concerning as-yet-unobserved values of x and y.

What Priest shows is that ‘certain very natural transformations’ on data sets result in different curves appearing to be ‘best’ and correspondingly conflicting predictions being delivered. Priest therefore claims to have shown that ‘which prediction is best depends not on the situation but how you describe it. (Equivalent descriptions do not give the same answers.)’ (p. 432). This sort of description-dependence sounds unsettling; we would like our predictions to be sensitive only to our data, and not affected by accidental features of the ways we happen to represent that data.

It seems to have been accepted in the subsequent literature that Priest’s problem, if it cannot be avoided, establishes a worrying kind of description-dependence. But in my opinion the existence of such description-dependence is not established by Priest’s argument. To get that conclusion, we would need an additional premise: that when we perform the transformations on the data that generate the new predictions, we are just redescribing the same situation, as opposed to considering a different situation.

Carl Ginet is running an excellent seminar here at Cornell on Timothy Williamson’s Knowledge and Its Limits. Here is a point that David Liebesman and I were pushing a couple of weeks ago against Williamson’s idea that knowledge is the most general factive mental state.

Imagine we discovered a community that had a word “schnow”, which is like our “know”. Their view about schnowledge is quite like our view about knowledge. For instance, they unhesitatingly say that Gettier cases are not cases of schnowledge. But they hold that there are fewer defeaters for schnowledge than we think there are for knowledge. For instance, in case like Harman’s example of the person who happens to not see the misleading newspapers saying the dictator is still alive, they will say that the person schnows that the dictator is dead. In general, it turns out, they don’t think that unobtained misleading evidence defeats schnowledge. They are, however, future externalists in the following sense. The fact that someone will obtain misleading evidence may defeat current schnowledge, though it doesn’t defeat current justification. I’m going to assume (perhaps wrongly!) that their view on schnowledge is strictly weaker than our view on knowledge, since we allow never unobtained misleading evidence to defeat knowledge, but strictly stronger than our view (and theirs) on justified true belief.

Now here are two questions for Williamson.

First, is schnowing that p a mental state? I can’t see anything in the arguments for knowledge being a mental state that would count against schnowledge being a mental state. Note, in particular, that it isn’t (easily) factorisable.

Second, is schowledge weaker than knowledge? That is, do they denote a weaker relation by ‘schnows’ than we denote by ‘knows’? I can see going either way here. On the one hand, they do use ‘schnows’ in a slightly different way to how we use ‘knows’. On the other, when it comes to normative terms, we are generally quite generous about allowing that people with different usage nevertheless have the same meaning. When Osama says, for instance, “Killing Christians is good”, he is falsely saying something using our common concept of goodness, not truly saying something using a different concept of goodness. Perhaps the people in question are just misusing ‘schnows’, or perhaps we are misusing ‘knows’.

But I think there is a problem for Williamson on either answer he gives to this question. If schnowledge is weaker than knowledge, then knowledge is not the most general factive mental state, because schnowledge is more general. If schnowledge is the same as knowledge, then it turns out our term ‘knows’ is not plastic. Small deviations, even large deviations, don’t produce a difference in denotation. But in Vagueness, his view was that vagueness in language is grounded in semantic plasticity. And it would be intolerable to say that ‘knows’ is not vague. So I don’t see a way to hold on both to the view that knowledge is the most general FMS, and the view that vagueness is a product of semantic plasticity.

Acer Nethercott sent along an interesting story about teaching philosophy to youngsters in Scotland. I’ve never been too confident of the utility of getting four year olds to worry about sceptical possibilities, but it looks like this program has long-term value.

And while I don’t have a link for this, this week’s TLS features reviews of two Australian philosophy books, Daniel Stoljar’s Ignorance and Imagination and Graham Oppy’s Philosophical Perspectives on Infinity.